Problem Statement 

John had two sons called Tom & Cruise. They have two arrays a & b of length n. They had to reverse at most one subarray (continuous subsegment) of the array a. Their task is to reverse the subarray in such a way that the sum $\displaystyle\sum_{i=1}^{n}$(a_i⋅b_i)is maximized.

Input

The first line contains one integer n (1≤n≤5000).

The second line contains n integers a₁,a₂,…,a_n(1≤a_i≤10⁷).

The third line contains n integers b₁,b₂,…,b_n (1≤b_i≤10⁷).

Output

Print single integer — maximum possible sum after reversing at most one subarray (continuous subsegment) of a